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Citrus2011 [14]

2 years ago

11

The trajectory of a flying saucer is given by the vector function r(t) = (5 sin(t))i + (5 cos(t))j + 12tk for t ≥ 0 where coordi

nate is measured in miles and time in minutes. Find the time moment t0 when the flying saucer travels exactly the distance 26 miles along the curve from the starting point.

1 answer:

Kipish [7]2 years ago

8 0

Answer:

t0 = 2

Step-by-step explanation:

r' = <5cost,-5sint,12>

ds = $\sqrt{25cos^{2}t+25sin^{2}t+12^2} = \sqrt{25+144} = 13$ dt

So, we want

$\int\limits^x_0 {13} \, dt = 26$

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Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$

Length of curve= $s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})$

Length of curve= $s=32.66$

5 0

2 years ago

Draw a line representing the "run" and a line representing the "rise" of the line. State the slope of the line in simplest form.

Igoryamba

Answer:

The answer is " $\bold{\frac{9}{13}}$ "

Step-by-step explanation:

In this question, the image file is missing, which is defined in the attached file. please find it.

$\to raise= y_2-y_1$

$=-1-(-10)\\\\=-1+10\\\\=9$

$\to run= x_2-x_1$

$=9-(-4)\\\\=9+4\\\\=13$

$\to \text{formula for slope} =\frac{rise}{run} =\frac{9}{13}$

7 0

2 years ago

Let X be a positive continuous random variable with density fXpxq. Let Y " lnpXq. (a) Find the density fY pyq of Y in terms of t

salantis [7]

Answer:

X density = fXpxq and

Y" =InpXq

Now to find Y density FYpyq interms of the density of X we compare the density of X with Y"

fX = In

And PXq =pxq

Thus replacing x with y,

PXq = pyq

(a) Hence the density of Y is FYpyq

(b) at p0, fYpyq =fYp0q= 0

At 5s, FYpyq =5

7 0

2 years ago

Read 2 more answers

Is (-3,11) a solution to the system of equation shown below.

natita [175]

No, when you substitute it into the first equation for x and y it does not equal 36 this it's not a solution

(-3)-(3)(11)=36
-3-33=36
-36 =/ 36

8 0

2 years ago

Can you guys help me with that ?

aleksley [76]

The shirts are 12.75 for 3 so we can write a ratio of $\frac{12.75}{3}$ To get the price of the shirts, one needs to divide $\frac{12.75}{3}$ , which will tells use what the unit price is per shirt. The price per shirt is $4.25

6 0

2 years ago